What is the method of finding the value of a variable in a system of equations where two or more simultaneous equations won’t intersect?

Asked Feb 16 '21 at 11:44

Active Feb 16 '21 at 11:44

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The question asks, “For what value of p will the lines 2x+3y=23 and 7x+py=8 not intersect?

I tried elimination and substitution but they both didn’t work (at least for me).

Is there any other method to work this out?

The answer provided by the textbook is p=10.5 and when I plugged it into a graphing calculator, the two lines were parallel.

asked Feb 16 '21 at 11:44

Somxr

Welcome to MSE. How did it not work? – José Carlos Santos Feb 16 '21 at 11:53
When do two lines not intersect? – P. J. Feb 16 '21 at 12:18
The methods I used (substitution, and elimination) gave me different answers – Somxr Feb 16 '21 at 12:42
I’m pretty sure that two lines will never intersect if they have the same gradient but a different constant. – Somxr Feb 16 '21 at 12:44
For each of them, rewrite them as $y=ax+b$ – Claude Leibovici Feb 16 '21 at 12:46
I rewrote them as 3y=-2x+23 and py=-7x+8 – Somxr Feb 16 '21 at 13:24

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